Programming Assignment 11.2.5 (1) Implement binomial tree algorithms for European knock-in and knock-out options with rebates. Pay special attention to convergence (see Fig. 11.5). Here is a solved problem: A down-and-in European call without rebates has a value of $5.6605 given S = 95, X= 100, H = 90, r = 10%

(continuously compounded), σ = 0.25, and τ = 1 (year). (2) Extend the algorithms to handle American barrier options.